The phrase used by George Bush during his campagin to show his more affectionate side. It's like a redneck shooting cans with a paintball gun rather than a rifle to be more affection. To get a better understanding read the story of the lions:

One day, one lion said to another "compassionate predator...i like it"

Compassionate conservative- Americans are hopeful that in Bush's second term, the compassionate side will kick in.

The phrase that attempts (unsuccessfully?)to force progressive ideas into a regressive box for the sole purpose of selling warm fuzzies to cold hearted bastards

Ghengis Khan's Mommy? Hitler on Christmas morning? Strom Thurmond while knocking boots with the domestic help? "The neo-fascist allowed the screaming young girl to look away as he hacked off her mother's head, justifying his reputation as a compassionate conservative."